Reading optics books there is sometimes a reference to the
radius of curvature of a paraboloid or some other non spherical curve. Since the
radius of the curve changes from center to edge how can this be? Finally I found
that if the zone of 'radius of curvature' of a lens or mirror is unspecified
they are generally referring to its 'radius of curvature' at its center.

If we plot the difference between a sphere and a parabola
zone by zone we get a curve like the top curve in the family of curves
above. If we specify that the reference sphere is not at the center but is
now at the 70 percent zone we get a difference curve like the middle curve
above. If the reference sphere has the 'radius of curvature' of the mirror edge
we get the bottom curve.

When doing the knife edge test it turns out that the
apparent
landscape of a parabolic mirror looks much like the shadows that would be
cast if a light were to be shining across these curves at a low angle.